After a long life in preprint form, Boardman's paper was published in the conference proceedings celebrating his 60th birthday:
  

      \bib{MR1718076}{article}{
           author={Boardman, J. Michael},
           title={Conditionally convergent spectral sequences},
           conference={
              title={Homotopy invariant algebraic structures},
              address={Baltimore, MD},
              date={1998},
           },
           book={
              series={Contemp. Math.},
              volume={239},
              publisher={Amer. Math. Soc., Providence, RI},
           },
           date={1999},
           pages={49--84},
           review={\MR{1718076}},
           doi={10.1090/conm/239/03597},
        }

In the $(s,d)$-bigraded case, you can replace Boardman's (left half-plane) condition that $E_1^{s,d} = 0$ for $s > 0$ (or $s > s_0$ for some fixed integer $s_0$) by the (upper half-plane) condition that $E_1^{s,d} = 0$ for all $d < 0$ (or $d < d_0$ for some fixed integer $d_0$).

Similarly, you can replace his (right half-plane) condition that $E_1^{s,d} = 0$ and $\bar E_1^{s,d} = 0$ for $s < 0$ (or $s < s_0$ for some fixed integer $s_0$) by the (lower half-plane) condition that $E_1^{s,d} = 0$ and $\bar E_1^{s,d} = 0$ for $d > 0$ (or $d > d_0$ for some fixed integer $d_0$).


To see this, you can basically reindex the filtration so as to move the internal degree $d$ part of filtration $s$ to filtration $s+d$, keeping the internal degree.  This shears the $E_1$-term, moving the vertical axis to the horizontal axis.

This adjustment is often enough.  Do you need to refer to other half-planes than those bounded by a horizontal or a vertical line?